SOLUTION: I have no clue how to start off with this problem. Any help would be great. Dish antennas have a parabolic cross-section. This concentrates signals onto a sensor at the focus of

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: I have no clue how to start off with this problem. Any help would be great. Dish antennas have a parabolic cross-section. This concentrates signals onto a sensor at the focus of      Log On


   



Question 1140704: I have no clue how to start off with this problem. Any help would be great.
Dish antennas have a parabolic cross-section. This concentrates signals onto a sensor at the focus of the parabola. A dish antenna is 1 meter wide and 20 centimeters deep. How far from the bottom of this dish should the sensor be positioned?

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Draw or sketch parabola with vertex at Origin, and vertex the minimum.
Two points are (0,0) and (1,20) (100, 20) (50, 20).

y=ax%5E2
-
a=y%2Fx%5E2
a=20%2F50%5E2
a=0.008
-
y=0.008x%5E2
Alternately expressed as highlight_green%28125y=x%5E2%29.

---the rest removed---

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are two problems with the solution by tutor @josgarithmetic:

(1) The "1" width is meters; the "20" depth is centimeters. You need to use consistent units. Changing the 1 meter to 100 centimeters, the second point on the parabola would be (100,20) instead of (1,20).

(2) The 100 centimeters is the total width of the parabola; the second point on the parabola is only half that distance from the vertex. The correct second point on the parabola is (50,20).

So now

y+=+%281%2F4p%29x%5E2

where p is the distance from the vertex (bottom of the dish) to the focus the sensor). Using the second point (50,20),

20+=+%281%2F4p%29%2850%5E2%29
1%2F4p+=+20%2F%2850%5E2%29+=+1%2F125
p+=+125%2F4

ANSWER: The sensor should be placed 125/4 = 31.25 cm from the bottom of the dish.